Recovery from electrode position uncertainties in geophysical electrical resistance tomography – Application to moisture transport imaging

In studies of subsurface hydrology, monitoring and imaging techniques are used to estimate the moisture content, or to track moisture or injected tracer movement. One applied imaging technique is electrical resistance tomography (ERT), in which measurements collected using electrodes placed on the ground surface or in boreholes are used to reconstruct the subsurface electrical conductivity, or its temporal changes. ERT image reconstructions are, however, very sensitive to measurement noise and especially modelling errors. In geophysical ERT, especially when using borehole electrodes, a significant modelling error may result from uncertain electrode positions. In this work, we study the effects of such modelling errors and apply the non‐linear difference (NLD) imaging and Bayesian approximation error approach to compensate for them. The approach is tested with numerical simulations representing tracer injection experiments into the subsurface. The results show that when electrode positions are uncertain, adopting the NLD imaging approach can yield feasible estimates for the conductivity change from the initial state in cases where the conventional linearized difference and absolute reconstructions are biased. Moreover, the study demonstrates that while the absolute values of the conductivity obtained by NLD imaging can be biased due to electrode position errors, enhancing the NLD reconstruction with Bayesian approximation error modelling improves the reconstruction of the initial conductivity and the temporal change of conductivity, leading to improvement in the absolute conductivity estimates.